Answer
Ellipse
Work Step by Step
Move $x^{2}$ and $y^{2}$ to the same side
$9(x+3)^{2}+4(y-2)^{2}=36$
Analysis:
$x^{2}$ and $y^{2}$ terms are same signs on the same side therefore equation is a circle or ellipse.
the $x^{2}$ term is scaled by 9 but the $y^{2}$ term is scaled by 4. These are at different rates therefore the equation is an ellipse.
